When I Open my Macbook Air, it recommend for the update from catalina 10.15.2. to 10.15.3, when I click for update it download the file and don't complete the update & not working & MAC book not starting.

Try Downloading and Installing the macOS Catalina 10.15.3 Combo Update. If you cannot boot your computer in order to do the aforementioned, then do the following:

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button.

This should install the same version of macOS that was already installed.